How to out run a coyoteBy B. Hughes

According to the California Wolf Centre website, a coyote can run as fast as 30 mph. This converts to a little over 13 m/s. In order to out run the coyote I plan on having enough of a head start that it will catch up to me just as I reach a vertical canyon wall. As I reach the wall, and just before it catches me, I will turn sharply to one side and the surprised coyote will run straight into the canyon wall. (In order to add to the surprise, earlier the same day I will paint a realistic picture of a tunnel on the canyon wall.)

Photo by Joe Dunckley

According to wikipedia the current world record for the 100 m sprint is “9.58 s is held by Usain Bolt of Jamaica, set at the 2009 World Athletics Championships.” This was an average speed of around 10 m/s. I suspect that my running speed will be lower than this, so I will assume I can run at 6 m/s. I also don't think I can run very far, so I will try to hide from the coyote until I am 25 metres away from the wall.

Here are the equations that describe our motion.

Me: xme=xmeo+V mex

t

Coyote: xC= xCo+V C xt

I set my starting position to xmeo=0 , the canyon wall is at x=+25m and I set the velocities of me

and the coyote to the values above. Plotting these equations using the Desmos.com graphing calculator, (you can view the graph and equations here: https://www.desmos.com/calculator/kazsicijyo ) I adjusted the starting position of the coyote until our graphs crossed right at the canyon wall at x=+25m . The graph is below.

Position(in m)

Me

CoyoteTime (in s)

The graph shows that I need a 30m head start in order to just make it to the wall as the coyote does. It also shows that I need to run for less than 5 seconds which I think I can do. The one thing that I left out is the acceleration from rest to out top speed for both me and the Coyote. This makes the problem much simpler but since I think the Coyote has a larger acceleration than me, it probably changes the final answer by several metres.

The Coyote drawing is by Pearson Scott Foresman and it is in the public domain.The running stick figure is modified from a drawing by Dominique Chappard which is in the public domain.

How to Outrun a Coyote by B. Hughes is licensed under a Creative Commons Attribution 3.0 Unported License.